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3 years ago

A submarine travels 7 km due East from its base and then turns and travels due North for 12.5

Mathematics

1 answer:

Maksim231197 [3]3 years ago

3 0

Answer:

The submarine is 10.4 km far from its base.

Step-by-step explanation:

Given that:

Distance traveled east = 7km

Distance traveled north = 12.5 km

This is will form a right triangle, where the distance from east to north is hypotenuse.

Here,

a = 7 , b = x and c = 12.5

Using Pythagorean theorem,

$a^2+b^2=c^2\\(7)^2+x^2=(12.5)^2\\49+x^2=156.25\\x^2=156.25-49\\x^2=107.25$

Taking square root on both sides

$\sqrt{x^2}=\sqrt{107.25}\\x=10.4$

Hence,

The submarine is 10.4 km far from its base.

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Alex17521 [72]

Answer:

x = 10 or x = 2

Step-by-step explanation:

Solve for x:

x^2 - 12 x + 20 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 20 from both sides:

x^2 - 12 x = -20

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 36 to both sides:

x^2 - 12 x + 36 = 16

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Take the square root of both sides:

x - 6 = 4 or x - 6 = -4

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Answer: x = 10 or x = 2

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3 years ago

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Illusion [34]

Answer:

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Step-by-step explanation:

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3 years ago

Who is farthest from the school

postnew [5]

Using the law of cosines:

The grocery store to the school:

Distance = √(7^2 + 10^2 - 2*7*10*cos(100)

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Distance = √(7^2 + 10^2 - 2*7*10*cos(120)

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4 years ago

Suppose you have 5 riders and 5 horses, and you want to pair them off so that every rider is assigned one horse (and no horse is

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There are 120 ways in which 5 riders and 5 horses can be arranged.

We have,

5 riders and 5 horses,

Now,

We know that,

Now,

Using the arrangement formula of Permutation,

i.e.

The total number of ways $^nN_r = \frac{n!}{(n-r)!}$ ,

So,

For n = 5,

And,

r = 5

As we have,

n = r,

So,

Now,

Using the above-mentioned formula of arrangement,

i.e.

The total number of ways $^nN_r = \frac{n!}{(n-r)!}$ ,

Now,

Substituting values,

We get,

$^5N_5 = \frac{5!}{(5-5)!}$

We get,

The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,

So,

There are 120 ways to arrange horses for riders.

Hence we can say that there are 120 ways in which 5 riders and 5 horses can be arranged.

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2 years ago

Luis has a pyramid shaped plant pot. It has a square base with a side length of 36\text{ cm}36 cm36, start text, space, c, m, en

harkovskaia [24]

Answer:

$15,552cm^3$

Step-by-step explanation:

Given

Side of length of the square base = 36cm

Height of the pyramid shaped plant pot = 36cm

Since the question does not specify what to look for, we can as well look for the volume of the pyramid shaped plant pot.

Volume of a pyramid = $\frac{Base\ area * Height}{3}$

Since the base is square

Base area = L²

Base area = 36²

Base area = 1296cm²

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Substituting the resulting values into the formula

$Volume = \frac{1296*36}{3}\\ \\volume = 1296*12\\\\Volume \ of \ the \ pyramid = 15,552cm^3$

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3 years ago